Photonic simulation of topological superconductor edge state and zero-energy mode at a vortex.

Tan W, Chen L, Ji X, Lin HQ - Sci Rep (2014)

Bottom Line:
Two essential characteristics of topological superconductor, particle-hole symmetry and p(x) + ip(y) pairing potentials, are well emulated in photonic systems.Its topological features are presented by chiral edge state and zero-energy mode at a vortex.This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.

ABSTRACTPhotonic simulations of quantum Hall edge states and topological insulators have inspired considerable interest in recent years. Interestingly, there are theoretical predictions for another type of topological states in topological superconductors, but debates over their experimental observations still remain. Here we investigate the photonic analogue of the p(x) + ip(y) model of topological superconductor. Two essential characteristics of topological superconductor, particle-hole symmetry and p(x) + ip(y) pairing potentials, are well emulated in photonic systems. Its topological features are presented by chiral edge state and zero-energy mode at a vortex. This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.

f1: Photonic simulation of TSC band structures.(a) A combination of electromagnetic duality and handedness inversion of photons mimics particle-hole transformation for electrons. For example, if a right-handed TE mode represent “particle”, a transformed left-handed TM mode can be considered as “hole”. (b,c) Band diagrams for particle-hole symmetric systems (b) without and (c) with px + ipy pairing potential. The px + ipy pairing potential leads to a gap with topological phase.

Mentions:
In general, the propagating waves in 2D can be classified into transverse electric (TE) mode and transverse magnetic (TM) mode. Thanks to electromagnetic duality of Maxwell's equations, equations for TE mode can be converted into that for TM mode by making transformations of Ez → Hz, Hx → −Ex, Hy → −Ey, ε → μ, and μ → ε. We suggest using band structures of TE and TM modes to mimic particle and hole states, respectively. However, electromagnetic duality is not enough for realizing photonic “particle-hole symmetry”, since particle-hole transformation also changes the sign of the kinetic energy. We design photonic band structures with positive- and negative-refractive-index bands by using metamaterials242526272829, which are also known as right-handed and left-handed bands, to mimic the positive- and negative-energy bands of particle and hole, respectively. In this way, the particle-hole transformation in condensed matter physics is emulated by a combination of electromagnetic duality and handedness inversion in photonics, as schematically shown in figure 1a. For example, a right-handed TE band and a well-designed left-handed TM band can present photonic “particle-hole symmetry”.

f1: Photonic simulation of TSC band structures.(a) A combination of electromagnetic duality and handedness inversion of photons mimics particle-hole transformation for electrons. For example, if a right-handed TE mode represent “particle”, a transformed left-handed TM mode can be considered as “hole”. (b,c) Band diagrams for particle-hole symmetric systems (b) without and (c) with px + ipy pairing potential. The px + ipy pairing potential leads to a gap with topological phase.

Mentions:
In general, the propagating waves in 2D can be classified into transverse electric (TE) mode and transverse magnetic (TM) mode. Thanks to electromagnetic duality of Maxwell's equations, equations for TE mode can be converted into that for TM mode by making transformations of Ez → Hz, Hx → −Ex, Hy → −Ey, ε → μ, and μ → ε. We suggest using band structures of TE and TM modes to mimic particle and hole states, respectively. However, electromagnetic duality is not enough for realizing photonic “particle-hole symmetry”, since particle-hole transformation also changes the sign of the kinetic energy. We design photonic band structures with positive- and negative-refractive-index bands by using metamaterials242526272829, which are also known as right-handed and left-handed bands, to mimic the positive- and negative-energy bands of particle and hole, respectively. In this way, the particle-hole transformation in condensed matter physics is emulated by a combination of electromagnetic duality and handedness inversion in photonics, as schematically shown in figure 1a. For example, a right-handed TE band and a well-designed left-handed TM band can present photonic “particle-hole symmetry”.

Bottom Line:
Two essential characteristics of topological superconductor, particle-hole symmetry and p(x) + ip(y) pairing potentials, are well emulated in photonic systems.Its topological features are presented by chiral edge state and zero-energy mode at a vortex.This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.

ABSTRACTPhotonic simulations of quantum Hall edge states and topological insulators have inspired considerable interest in recent years. Interestingly, there are theoretical predictions for another type of topological states in topological superconductors, but debates over their experimental observations still remain. Here we investigate the photonic analogue of the p(x) + ip(y) model of topological superconductor. Two essential characteristics of topological superconductor, particle-hole symmetry and p(x) + ip(y) pairing potentials, are well emulated in photonic systems. Its topological features are presented by chiral edge state and zero-energy mode at a vortex. This work may fertilize the study of photonic topological states, and open up the possibility for emulating wave behaviors in superconductors.